Chapter 27 - Part IX - The Basic Tools of Finance - Problems and Applications - Page 582: 2

a) 11%--no, 10%--yes, 9%--yes, 8%--yes b) 10.67%

cost of project = 10 million dollars payoff time = 4 years payoff value = 15 million dollars a) interest rate = 8% $10000000*(1+.08)^4$ $10000000*1.08^4$ $10000000*1.36048896$ $13,604,889.60$ Since this value is less than the payoff value, then the company should undertake the project. Interest rate = 9% $10000000*(1+.09)^4$ $10000000*1.09^4$ $10000000*1.41158161$ $14,115,816.10$ Since this value is less than the payoff value, then the company should undertake the project. Interest rate = 10% $10000000*(1+.10)^4$ $10000000*1.1^4$ $10000000*1.4641$ $14,641,000$ Since this value is less than the payoff value, then the company should undertake the project. Interest rate = 11% $10000000*(1+.11)^4$ $10000000*1.11^4$ $10000000*1.51807041$ $15,180,704.10$ Since this value is greater than the payoff value, then the company should not undertake the project. b) $1000000*(1+x)^4=15000000$ $1000000*(1+x)^4/10000000=15000000/10000000$ $(1+x)^4=1.5$ $\sqrt{(1+x)^4} = \sqrt 1.5$ $(1+x)^2 = 1.224745$ $\sqrt {(1+x)^2} = \sqrt {1.224745}$ $1+x = 1.10668$ $1+x-1=1.10668-1$ $x = .10668$ At an interest rate of 10.668%, the project is at break-even. It is at this interest rate where the project is between profitability and non-profitability.